Sensitivity analysis of electromagnetic measurements over exponentially varying conductivity earth models

Sensitivity analysis of electromagnetic (EM) measurements is important to quantify the effect of the subsurface conductivity on the measured response. Knowledge of the sensitivity functions helps in solving inverse problems related to field data. In the present paper, we have derived the sensitivity functions for exponentially varying conductivity earth models. The effect of the exponential variation of conductivity has been illustrated graphically on the sensitivity functions. The effect of varying the periods of the electromagnetic waves on the sensitivity functions has also been studied, which gives the characteristic behaviour of the sensitivity functions. This characteristic behaviour provides information about the exponentially decreasing or increasing conductivity earth models.     

Interpretation of long-offset transient electromagnetic data from the Odenwald area, Germany, using two-dimensional modelling

The standard 1-D inversion approach for the interpretation of transient electromagnetic (TEM) data usually fails in the presence of near-surface conductivity anomalies. Since multidimensional inversion codes are not routinely available, the only alternative to discarding the data may be trial-and-error forward modelling. We interpret data from a long-offset transient electromagnetic (LOTEM) survey which was carried out in 1995 in the Odenwald area, using 2-D finite-difference modelling. We focus on a subsegment of the LOTEM profile, which was shot with two different electric dipole transmitters. A model is found which consistently explains the electric and magnetic field data at eight locations for both transmitters. First, we introduce a conductive dyke under the receiver spread to explain sign reversals in the magnetic field transients. A conductive slab under one of the transmitters is required to obtain a reasonable quantitative fit for that transmitter. Consideration of the electric field data then requires a modification of the layered earth background. Finally, we study the response of a crustal conductor, which was the original target of the survey. The data are sensitive to the conductor, and for the investigated subset of the data the fits are slightly better without the conductive layer.     

Forward modelling of direct current and low-frequency electromagnetic fields using integral equations

We present a semi-analytical, unifying approach for modelling the electromagnetic response of 3-D bodies excited by low-frequency electric and magnetic sources. We write the electric and magnetic fields in terms of power series of angular frequency, and show that to obey Maxwell's equations, the fields must be real when the exponent is even, and imaginary when it is odd. This leads to the result that the scattering equations for direct current fields and for fields proportional to frequency can both be explicitly formulated using a single, real dyadic Green's function. Although the underground current flow in each case is due to different physical phenomena, the interaction of the scattering currents is of the same type in both cases. This implies that direct current resistivity, magnetometric resistivity and electric and magnetic measurements at low induction numbers can all be modelled in parallel using basically the same algorithm. We make a systematic derivation of the quantities required and show that for these cases they can all be expressed analytically. The problem is finally formulated as the solution of a system of linear equations. The matrix of the system is real and does not depend on the type of source or receiver. We present modelling results for different arrays and apply the algorithm to the interpretation of field data. We assume the standard dipoledipole resistivity array for the direct current case, and vertical and horizontal magnetic dipoles for induction measurements. In the case of magnetometric resistivity we introduce a moving array composed of an electric dipole and a directional magnetometer. The array has multiple separations for depth discrimination and can operate in two modes. The mode where the predominant current flow runs along the profile is called MMR-TM. This mode is more sensitive to lateral variations in resistivity than its counterpart, MMR-TE, where the mode of conduction is predominantly perpendicular to the profile.     

Electromagnetic induction studies in the Eyre Peninsula, South Australia

Magnetic field fluctuations have been recorded by an array of portable three-component magnetometers at 60 sites across the Eyre Peninsula in South Australia between December 1993 and March 1995. An additional 54 magnetometer data records, collected prior to 1989 and described by Milligan (1989) and Milligan, White & Chamalaun (1989), were included in the analysis. A major conductive feature in the crust, first noted by White & Milligan (1984) as the Eyre Peninsula Anomaly (EPA), is re-examined to assess its continuity to the north of the original arrays and to investigate its relationship with major tectonic features.
Magnetic-field time-series were converted to induction arrows in the frequency domain. These induction arrows were initially inverted using the minimum-structure 2-D Occam approach to estimate the electrical conductance of the crust. Following this, thin-sheet forward modelling was used to examine the relationship between the conductance and the dominant tectonic features. The principal results of the modelling are that a narrow conductive feature extends inland from the coast about 160 km before terminating, and the conductance is in the range 3000 to 10 000 S, which decreases inland.
A strong correlation exists between the electrical conductance of the Eyre Peninsula and Bouguer gravity anomalies, and in particular the EPA is coincident with a significant Bouguer gravity gradient. There is also good agreement between the locations of the foci of earthquakes of magnitude greater than 4.0 and the EPA. We believe that the anomaly is associated with a geological fracture in the Precambrian upper crust as a result of crustal extension prior to the rifting of Australia from Antarctica in the Jurassic (160 Ma).     

Long-period (30 days1 year) electromagnetic sounding and the electrical conductivity of the lower mantle beneath Europe

The C -response connects the magnetic vertical component and the horizontal gradient of the horizontal components of electromagnetic variations and forms the basis for deriving the conductivitydepth profile of the Earth. Time-series of daily mean values at 42 observatories typically with 50 years of data are used to estimate C -responses for periods between 1 month and 1  yr. The Z : Y method is applied, which means that the vertical component is taken locally whereas the horizontal components are used globally by expansion in a series of spherical harmonics.
In combination with results from previous analyses, the method yields consistent results for European observatories in the entire period range from a few hours to 1  yr, corresponding to penetration depths between 300 and 1800  km.
1-D conductivity models derived from these results show an increase in conductivity with depth z to about 2  S  m^-1 at z =800  km, and almost constant conductivity between z =800 and z =2000  km with values of 310  S  m^-1, in good agreement with laboratory measurements of mantle material. Below 2000  km the conductivity is poorly resolved. However, the best-fitting models indicate a further increase in conductivity to values between 50 and 150  S  m^-1.     

Subspace inversion of electromagnetic data: application to mid-ocean-ridge exploration

Controlled-source electromagnetic (CSEM) surveys have the ability to provide tomo-graphic images of electrical conductivity within the Earth. the interpretation of such data sets has long been hampered by inadequate modelling and inversion techniques. In this paper, a subspace inversion technique is described that allows electric dipole-dipole data to be inverted for a 2-D electrical conductivity model more efficiently than with existing techniques. the subspace technique is validated by comparison with conventional inversion methods and by inverting data collected over the East Pacific Rise in 1989. A model study indicates that, with adequate data, a variety of possible mid-ocean-ridge conductivity models could be distinguished on the basis of a CSEM survey.     

Geoelectromagnetic induction in a heterogeneous sphere:a new three-dimensional forward solver using a conservative staggered-grid finite difference method

A conservative staggered-grid finite difference method is presented for computing the electromagnetic induction response of an arbitrary heterogeneous conducting sphere by external current excitation. This method is appropriate as the forward solution for the problem of determining the electrical conductivity of the Earth's deep interior. This solution in spherical geometry is derived from that originally presented by Mackie et al. (1994 ) for Cartesian geometry. The difference equations that we solve are second order in the magnetic field H , and are derived from the integral form of Maxwell's equations on a staggered grid in spherical coordinates. The resulting matrix system of equations is sparse, symmetric, real everywhere except along the diagonal and ill-conditioned. The system is solved using the minimum residual conjugate gradient method with preconditioning by incomplete Cholesky decomposition of the diagonal sub-blocks of the coefficient matrix. In order to ensure there is zero H divergence in the solution, corrections are made to the H field every few iterations. In order to validate the code, we compare our results against an integral equation solution for an azimuthally symmetric, buried thin spherical shell model ( Kuvshinov & Pankratov 1994 ), and against a quasi-analytic solution for an azimuthally asymmetric configuration of eccentrically nested spheres ( Martinec 1998 ).